Empirical CDF
Calculate the step CDF for a finite sample with ties and observe right-continuity.
Free theory articleCalculate the step CDF for a finite sample with ties and observe right-continuity.
Concept & interpretation
The Empirical Cumulative Distribution Function (ECDF) is a step function that estimates the true cumulative distribution function of the population that generated the sample. For a dataset of n observations, the empirical CDF at any value x is the proportion of the sample that is less than or equal to x.
Experiment
You can use the Empirical CDF interactive module to observe how the step plot changes based on your data.
- Select the Ties preset to load the sample
1, 2, 2, 4. - Set the threshold slider to exactly
2.0. - Observe that the calculated CDF value F_n(2.0) is exactly 0.75, showing that the function counts the tied values up to and including the threshold.
- Select the Single observation preset to observe how a single data point creates a single unit jump from 0 to 1 at its location.